Quantum phase transitions of interacting bosons on hyperbolic lattices

TL;DR

This paper investigates quantum phase transitions of interacting bosons on hyperbolic lattices, revealing how the lattice geometry influences phase stability and transitions, with implications for ultracold atom experiments.

Contribution

It provides the first detailed phase diagram of the extended Bose-Hubbard model on hyperbolic lattices, highlighting the role of coordination number in quantum phase transitions.

Findings

Mott lobes shrink with increasing q

Supersolid phase is stabilized at smaller interactions

Hyperbolic lattices offer a unique platform for studying coordination effects

Abstract

The effect of many-body interaction in curved space is studied based on the extended Bose--Hubbard model on hyperbolic lattices. Using the mean-field approximation and quantum Monte Carlo simulation, the phase diagram is explicitly mapped out, which contains the superfluid, supersolid and insulator phases at various fillings. Particularly, it is revealed that the sizes of the Mott lobes shrink and the supersolid is stabilized at smaller nearest-neighbor interaction as $q$ in the Schl\"afli symbol increases. The underlying physical mechanism is attributed to the increase of the coordination number, and hence the kinetic energy and the nearest-neighbor interaction. The results suggest that the hyperbolic lattices may be a unique platform to study the effect of the coordination number on quantum phase transitions, which may be relevant to the experiments of ultracold atoms in optical lattices.